code: def test_zeta_eval():
      assert zeta(nan) is nan
      assert zeta(x, nan) is nan
  
      assert zeta(0) == Rational(-1, 2)
      assert zeta(0, x) == S.Half - x
      assert zeta(0, b) == S.Half - b
  
      assert zeta(1) is zoo
      assert zeta(1, 2) is zoo
      assert zeta(1, -7) is zoo
      assert zeta(1, x) is zoo
  
      assert zeta(2, 1) == pi**2 / 6
      assert zeta(3, 1) == zeta(3)
  
      assert zeta(2) == pi**2 / 6
      assert zeta(4) == pi**4 / 90
      assert zeta(6) == pi**6 / 945
  
      assert zeta(4, 3) == pi**4 / 90 - Rational(17, 16)
      assert zeta(7, 4) == zeta(7) - Rational(282251, 279936)
      assert zeta(S.Half, 2).func == zeta
      assert expand_func(zeta(S.Half, 2)) == zeta(S.Half) - 1
      assert zeta(x, 3).func == zeta
      assert expand_func(zeta(x, 3)) == zeta(x) - 1 - 1 / 2**x
  
      assert zeta(2, 0) is nan
      assert zeta(3, -1) is nan
      assert zeta(4, -2) is nan
  
      assert zeta(oo) == 1
  
      assert zeta(-1) == Rational(-1, 12)
      assert zeta(-2) == 0
      assert zeta(-3) == Rational(1, 120)
      assert zeta(-4) == 0
      assert zeta(-5) == Rational(-1, 252)
  
      assert zeta(-1, 3) == Rational(-37, 12)
      assert zeta(-1, 7) == Rational(-253, 12)
      assert zeta(-1, -4) == Rational(-121, 12)
      assert zeta(-1, -9) == Rational(-541, 12)
  
      assert zeta(-4, 3) == -17
      assert zeta(-4, -8) == 8772
  
      assert zeta(0, 1) == Rational(-1, 2)
      assert zeta(0, -1) == Rational(3, 2)
  
      assert zeta(0, 2) == Rational(-3, 2)
      assert zeta(0, -2) == Rational(5, 2)
  
      assert (
          zeta(3)
          .evalf(20)
          .epsilon_eq(Float("1.2020569031595942854", 20), 1e-19)
      )
  
imports: from sympy.concrete.summations import Sum
  from sympy.core.function import expand_func
  from sympy.core.numbers import Float, I, Rational, nan, oo, pi, zoo
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol
  from sympy.functions.elementary.complexes import Abs, polar_lift
  from sympy.functions.elementary.exponential import exp, exp_polar, log
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.special.zeta_functions import dirichlet_eta, lerchphi, polylog, riemann_xi, stieltjes, zeta
  from sympy.series.order import O
  from sympy.core.function import ArgumentIndexError
  from sympy.functions.combinatorial.numbers import bernoulli, factorial, genocchi, harmonic
  from sympy.testing.pytest import raises
  from sympy.core.random import test_derivative_numerically, random_complex_number, verify_numerically
label_desc: Use image node_id 1 for calling a global function with example usage: test_zeta_eval() without return types